Data-Driven Wall Pressure Reconstruction and Sparse Sensor Optimization for Supersonic Nozzles

Accurate reconstruction of aerodynamic forces from sparse wall pressure sensor inputs presents significant challenges for monitoring supersonic nozzles, where the flow is characterized by intense nonlinearity and transient flow patterns under varying nozzle pressure ratios (NPR). Limited by the geometric constraints of nozzle contours and measurement cost, reconstructing the pressure distribution through sparse sensors has become critically important. This study presents a data-driven wall pressure reconstruction model based on a small number of pressure sensors on the surface of a supersonic nozzle wall. In this context, we advance data-driven methodologies by rigorously comparing two sparse sensor paradigms: discrete empirical interpolation method with proper orthogonal decomposition (DEIM-POD) and compressed sensing-POD (CS-POD). Through wind-tunnel experiments on an axisymmetric expansion nozzle, we demonstrate DEIM-POD’s superior performance: achieving 30% lower reconstruction errors than the vectorized CS-POD (Vec-CS-POD) at equivalent sensor densities while maintaining NPR adaptability with fixed sensor arrays. Additionally, this method can resolve shock-induced intense pressure gradients well and operates in practical configurations requiring 60% fewer sensors than conventionally uniformly spaced sensor layouts. Computational efficiency analyses reveal that DEIM-POD’s greedy sampling executes faster than CS-POD’s randomized approach. To address localized sensor failures, we also introduce a geometrically constrained DEIM variant, namely modified DEIM-POD, which improves missing-data robustness and a comparable error level compared to the DEIM-POD model. These findings establish DEIM-POD as a preferred and potential framework, balancing measurement economy with reconstruction fidelity in supersonic flow applications.